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Substituting la and solving for Tw, we get: |
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We can rewrite this in terms of f: |
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and we can find ra in terms of the preceding: |
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Suppose there are multiple disk servers (m). Now, accesses may or may not be uniformly distributed across these servers. Requests often cluster to a single file, and thus, despite the existence of multiple servers, the system may reference only one (or at least a smaller number than the physical number of servers). We will discuss this issue later in the chapter. For the moment, assume that m represents the effective number of independent servers. It is clear that: |
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Number of physical servers ³ m ³ 1. |
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Now, if requests are uniformly distributed over these m servers, the offered request rate l is reduced by a factor of m. |
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So we rewrite Equation (9.5) as: |
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Thus, for multiple servers, we rewrite equations (9.6)(9.8) as: |
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